> Questions: Will MathML facilitate complicated equations as does LaTeX?
> Is it conceivable that LaTeX equations may be entered within
> special MathML tag(s) so that conversion is done "behind the scenes"?
As others have said, basically the answers to both those questions are
yes.
In addition to authoring in latex and converting to MathML, you also have
the option of authoring in MathML and converting to latex.
LaTeX is definitely easier to author than MathML if you are just using a
text editor (although authoring MathML just in emacs isn't so bad: we do
a fair amount of that here:-) however there are other options, eg
several commercial or free projects to produce more or less wysiwyg
MathML editing, or saving MathML from systems such as Mathematica or
maple.
Even if authoring in MathML just in a text editor, the benefits that you
gain over going in the other direction are much tighter control over the
input (latex doesn't really have much of a notion of validation)
and an easier conversion route.
It's definitely easier to convert MathML to latex than to go in the
other direction, as the input is far more structured.
Which direction latex->MathML or MathML->latex is better depends on
several things, not least personal preference, so there isn't a
simple recommendation that can be given.
As far as expressivity for complicated expressions goes, MathML has
essentially enough constructs to lay out mathematics as well as TeX.
Whether a particular renderer lays them out well is of course a feature
of that renderer; unlike TeX which is only designed to work with one
layout engine. the only MathML renderer that I'm prepared to comment on
in public is the one I implemented in pmathmlcss.xsl available from the
W3C site, which uses CSS and javascript to display MathML in a web
browser, the typographic quality there is considerably worse than that of
TeX, but as it's only intended as a last fallback if nothing else is
available...
The main difficulty is multi line displayed mathematics, the problem
here is not so much a difference between the languages, so much as the
way they are used:
The TeXbook says of this:
It's quite an art to decide how to break long displayed formulas into
several lines; TeX never attempts to break them, because no set of
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
rules is really adequate. The author of a mathematical manuscript is
generally the best judge of what to do, since break positions depend
on subtle factors of mathematical exposition. For example, it is often
desirable to emphasize some of the symmetry or other structure that
underlies a formula, and such things require a solid understanding of
exactly what is going on in that formula.
So in TeX all line breaking is manual, and in LaTeX we have the many
different flavour of alignment possibilities given by the amsmath
package for example.
MathML probably has enough alignment primitives to mimic that (although
not all systems currently support malign in its full form, you can get a
long way just with mtable) however in many cases you _don't_ want to do
this. In TeX it is reasonable for the author to have full control as the
document is targeted at a particular page size, set of fonts, etc, but
in MathML, while one could use MathML to target a particular document
renderer the mindset is that you should be writing a multi use document
that still works, even if the reader resizes the window, or choses a
larger font set (or is using an audio renderer).
This means that when converting from LaTeX you have to make a choice
of trying to preserve your carefully tuned manual breaks in the MathML
or whether to lose them and live with the possibly less optimal breaks
produced by the formatter, both of those choices are possible but
deciding which one to take isn't always easy. Especially if (as often
happens) the LaTeX markup isn't sufficiently clean that you can
easily tell if the multi-line display really does logically need to be
on several lines (eg a set of simultaneous equations) or whether it is
really just a long equation broken so that it fits a particular page
size.
David
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